crandep (version 0.3.11)

dmix3: Probability mass function (PMF) of 3-component discrete extreme value mixture distribution

Description

dmix3 returns the PMF at x for the 3-component discrete extreme value mixture distribution. The component below v is the (truncated) Zipf-polylog(alpha1,theta1) distribution, between v & u the (truncated) Zipf-polylog(alpha2,theta2) distribution, and above u the generalised Pareto(shape, sigma) distribution.

Usage

dmix3(x, v, u, alpha1, theta1, alpha2, theta2, shape, sigma, phi1, phi2, phiu)

Value

A numeric vector of the same length as x

Arguments

x

Vector of positive integers

v

Positive integer representing the lower threshold

u

Positive integer representing the upper threshold

alpha1

Real number, first parameter of the Zipf-polylog component below v

theta1

Real number in (0, 1], second parameter of the Zipf-polylog component below v

alpha2

Real number, first parameter of the Zipf-polylog component between v & u

theta2

Real number in (0, 1], second parameter of the Zipf-polylog component between v & u

shape

Real number, shape parameter of the generalised Pareto component

sigma

Real number, scale parameter of the generalised Pareto component

phi1

Real number in (0, 1), proportion of values below v

phi2

Real number in (0, 1), proportion of values between v & u

phiu

Real number in (0, 1), exceedance rate of the threshold u

See Also

Smix3 for the corresponding survival function, dpol and dmix2 for the PMFs of the Zipf-polylog and 2-component discrete extreme value mixture distributions, respectively.